Geometric phase and nonadiabatic effects in an electronic harmonic oscillator

Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.     

Coherence times of dressed states of a superconducting qubit under extreme driving

We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, and an intense microwave field. The dressed states represent the hybridization of the qubit and photon degrees of freedom and appear as avoided level crossings in the combined energy diagram. By embedding the circuit in an rf oscillator, we directly probe the dressed states. We measure their dressed gap as a function of photon number and microwave amplitude, finding good agreement with theory. In addition, we extract the relaxation and dephasing rates of these states.     

ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field

We have performed spectroscopy of a superconducting charge qubit coupled nonresonantly to a single mode of an on-chip resonator. The strong coupling induces a large ac Stark shift in the energy levels of both the qubit and the resonator. The dispersive shift of the resonator frequency is used to nondestructively determine the qubit state. Photon shot noise in the measurement field induces qubit level fluctuations leading to dephasing which is characteristic for the measurement backaction. A crossover in line shape with measurement power is observed and theoretically explained. For weak measurement a long intrinsic dephasing time of T2>200 ns of the qubit is found.     

Quantum nondemolition measurements of a flux qubit coupled to a noisy detector

We theoretically study the quantum nondemolition measurements of a flux qubit coupled to a noisy superconduct-ing quantum interference device (SQUID).The obtained analytical results indicate that the measurement probability is frequency-dependent in a short time scale and has a close relationship with the measurement-induced dephasing.Furthermore,when the detuning between the driven and bare resonator equals the coupling strength,we can obtain the maximum measurement rate that is determined by the character of the noise in the SQUID.Finally,we analysed the mixed effect caused by coupling between the non-diagonal term and the external variable.It is found that the initial information of the qubit is destroyed due to quantum tunneling between the qubit states.     

Optimal quantum estimation of the coupling constant of Jaynes-Cummings interaction

We address the estimation of the coupling constant of the Jaynes-Cummings Hamiltonian for a coupled qubit-oscillator system. We evaluate the quantum Fisher Information (QFI) for the system undergone the Jaynes-Cummings evolution, considering that the probe initial state is prepared in a Fock state for the oscillator and in a generic pure state for the qubit; we obtain that the QFI is exactly equal to the number of excitations present in the probe state. We then focus on the two subsystems, namely the qubit and the oscillator alone, deriving the two QFIs of the two reduced states, and comparing them with the previous result. Next we focus on possible measurements on the system, and we find out that if population measurement on the qubit and Fock number measurement on the oscillator are performed together, the Cramer-Rao bound is saturated, that is the corresponding Fisher Information (FI) is always equal to the QFI. We compare also the performances of these energy measurements performed alone, that is when one of the two subsystem is ignored. We show that, when the qubit is prepared in either the ground or the excited state, the local measurements are still optimal. Finally we investigate the case when the harmonic oscillator is prepared in a thermal state and observe how, particularly for small values of the coupling constant, the QFI increases with the average number of thermal photons of the initial state.     

Correlations between quantum and stochastic systems with a dephasing coupling

Correlations between single qubit and classical environment are studied by means of the stochastic Liouville equation, where a dephasing coupling between them is assumed. When the dephasing of the qubit is characterized by the two-state-jump Markov process, the properties of the total, classical and quantum correlations are examined.     

Single-qubit lasing and cooling at the Rabi frequency

For a superconducting qubit driven to perform Rabi oscillations and coupled to a slow electromagnetic or nanomechanical oscillator we describe previously unexplored quantum optics effects. When the Rabi frequency is tuned to resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and a bistability with lasing behavior of the oscillator; for red detuning the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit-oscillator coupling is quadratic and decoherence effects are minimized. There the system realizes a "single-atom-two-photon laser."     

Synchronization and bistability of a qubit coupled to a driven dissipative oscillator

We study numerically the behavior of a qubit coupled to a quantum dissipative driven oscillator (resonator). Above a critical coupling strength the qubit rotations become synchronized with the oscillator phase. In the synchronized regime, at certain parameters, the qubit exhibits tunneling between two orientations with a macroscopic change of the number of photons in the resonator. The lifetimes in these metastable states can be enormously large. The synchronization leads to a drastic change of qubit radiation spectrum with the appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev, Nature (London) 449, 588 (2007)].     

Lasing without inversion in circuit quantum electrodynamics

We study the photon generation in a transmission line oscillator coupled to a driven qubit in the presence of a dissipative electromagnetic environment. It has been demonstrated previously that a population inversion in the qubit can lead to a lasing state of the oscillator. Here we show that the circuit can also exhibit the effect of "lasing without inversion." It arises since the coupling to the dissipative environment enhances photon emission as compared to absorption, similar to the recoil effect predicted for atomic systems. While the recoil effect is very weak, and so far elusive, the effect described here should be observable with realistic circuits. We analyze the requirements for system parameters and environment.     

The effects of LO phonons on charge qubit

In this paper, we study the influence of LO phonon (LOP) on the charge qubit in a quantum dot (QD), and find that the eigenenergies of the ground and first excited states are reduced due to the electron-LOP interaction. At the same time, the time evolution of the electron probability density is obtained, the dependence of the oscillating period on electron-LOP coupling constant is found, the relation of between the oscillating period and the confinement length of the QD is calculated. Finally, we consider the effects of the electron-LOP coupling constant on pure dephasing factor under considering the correction of electron-LOP interaction for the wave functions. Our results suggest that electron-LOP interaction has very important effects on charge qubit.     

Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole

We study the dynamical decoherence of a qubit weakly coupled to a two-body random interaction model (TBRIM) describing a quantum dot of interacting fermions or the Sachdev–Ye–Kitaev (SYK) black hole model. We determine the rates of qubit relaxation and dephasing for regimes of dynamical thermalization of the quantum dot or of quantum chaos in the SYK model. These rates are found to correspond to the Fermi golden rule and quantum Zeno regimes depending on the qubit–fermion coupling strength. An unusual regime is found where these rates are practically independent of TBRIM parameters. We push forward an analogy between TBRIM and quantum small-world networks with an explosive spreading over exponentially large number of states in a finite time being similar to six degrees of separation in small-world social networks. We find that the SYK model has approximately two–three degrees of separation.     

Fabrication and characterization of superconducting multiqubit device with niobium base layer

Superconducting transmon qubits are the leading platform in solid-state quantum computing and quantum simulation applications. In this work, we develop a fabrication process for the transmon multiqubit device with a niobium base layer,shadow-evaporated Josephson junctions, and airbridges across the qubit control lines to suppress crosstalk. Our results show that these multiqubit devices have well-characterized readout resonators, and that the energy relaxation and Ramsey(spin-echo) dephasing times are up to ～40 μs and 14(47) μs, respectively. We perform single-qubit gate operations that demonstrate a maximum gate fidelity of 99.97%. In addition, two-qubit vacuum Rabi oscillations are measured to evaluate the coupling strength between qubits, and the crosstalk among qubits is found to be less than 1% with the fabricated airbridges. Further improvements in qubit coherence performance using this fabrication process are also discussed.     

Vacuum Rabi oscillations in a macroscopic superconducting qubit oscillator system

We have observed the coherent exchange of a single energy quantum between a flux qubit and a superconducting LC circuit acting as a quantum harmonic oscillator. The exchange of an energy quantum is known as the vacuum Rabi oscillation: the qubit is oscillating between the excited state and the ground state and the oscillator between the vacuum state and the first excited state. We also show that we can detect the state of the oscillator with the qubit and thereby obtained evidence of level quantization of the LC circuit. Our results support the idea of using oscillators as couplers of solid-state qubits.     

Engineering decoherence in Josephson persistent-current qubits

We discuss the relaxation and dephasing rates that result from the control and the measurement setup itself in experiments on Josephson persistent-current qubits. For control and measurement of the qubit state, the qubit is inductively coupled to electromagnetic circuitry. We show how this system can be mapped on the spin-boson model, and how the spectral density of the bosonic bath can be derived from the electromagnetic impedance that is coupled to the qubit. Part of the electromagnetic environment is a measurement apparatus (DC-SQUID), that is permanently coupled to the single quantum system that is studied. Since there is an obvious conflict between long coherence times and an efficient measurement scheme, the measurement process is analyzed in detail for different measurement schemes. We show, that the coupling of the measurement apparatus to the qubit can be controlled in situ. Parameters that can be realized in experiments today are used for a quantitative evaluation, and it is shown that the relaxation and dephasing rates that are induced by the measurement setup can be made low enough for a time-resolved study of the quantum dynamics of Josephson persistent-current qubits. Our results can be generalized as engineering rules for the read-out of related qubit systems. Received 4 September 2002 Published online 27 January 2003 RID="a" ID="a"Present address: Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA RID="b" ID="b"Present address: Sektion Physik and CeNS, Ludwig-Maximilians Universit?t, Theresienstr. 37, 80333 Munich, Germany e-mail: wilhelm@theorie.physik.uni-muenchen.de     

Relaxation and dephasing in a many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a fluctuating force generated by a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate Green's functions and discuss relaxation and dephasing of a single extra particle added above the Fermi sea. We also extend our analysis to a more generic coupling between system and bath that results in complete thermalization of the system.     

Tailoring the ultrafast dephasing of quasiparticles in metallic photonic crystals

The ultrafast dephasing of waveguide-plasmon polaritons in metallic photonic crystal slabs is investigated in the femtosecond regime by second-order nonlinear autocorrelation. We find a drastic modification of the dephasing rates due to interaction between localized particle plasmons and optical waveguide modes and subsequent modification of the photonic density of states. In the strong coupling regime our measurements give clear evidence for the appearance of ultrafast polaritonic beat phenomena. All experimental results agree well with theoretical simulations based on a coupled damped harmonic oscillator model.     

Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit

We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare the performance of Hahn, CP, concatenated dynamical decoupling (CDD), and Uhrig dynamical decoupling for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T(2)～80 μs.     

Optimal dynamical decoherence control of a qubit

We present a theory of dynamical control by modulation for optimal decoherence reduction. The theory is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.     

Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap

Based on single Cesium atoims trapped in a 1064 nm microscopic optical trap we have exhibited a single qubit encoded in the Cesium ＂clock states＂. The single qubit initialization, detection and the fast state rotation with high efficiencies are demonstrated and this state manipulation is crucial for quantmn information processing. The ground ~ates Rabi flopping rate of 229.0 ± 0.6 kHz is realized hy a two-photon Raman process. A clock states dephasing time of 3.0 ± 0.7 ms is measured, while all irreversible homogeneous dephasing time of 124 ± 17 ms is achieved by using the spin-echo technique. This well-controlled single atom provides an ideal quantmn qubit and quantmn node for quantum information processing.